In 30 seconds
The 2021 Summer of Math Exposition encouraged creators to explain mathematics in many formats. The narrator discusses five selections, honorable mentions and the value of sharing clear ideas beyond a contest.
- 1Participation is the goalThe event aims to create more helpful math explanations, not merely select winners.
- 2A large review effortPeer reviewers and guest judges helped assess over 1,200 submissions.
- 3Stories support explanationA narrative can connect familiar puzzles to deeper mathematical ideas.
Takeaways
- The event’s goal was to encourage mathematical exposition, not just competition.
- Clear intuition and well-chosen examples matter more than production polish alone.
- Submissions used video, writing and interactive formats.
- Stories can connect everyday puzzles to deeper mathematics.
Read the edited text by chapter
Why the event exists
3Blue1Brown’s narrator and James Schloss organized the 2021 Summer of Math Exposition to encourage people to create online explanations of mathematics. The contest accepted many formats, subjects and audiences.
3Blue1Brown’s narrator and James Schloss organized the 2021 Summer of Math Exposition to encourage people to create online explanations of mathematics. The contest accepted many formats, subjects and audiences.
The narrator cautions against treating winning as the purpose. A deadline and small stakes can help people finish carefully, but success means more useful and engaging explanations exist for future learners.
More than 1,200 submissions arrived. Peer review narrowed them to a little over 100 for close examination, and guest judges helped with the final choices. Schloss was the central organizer.
Five selected works
One selected video by Paralogical starts with the bright curve at the bottom of a mug and explains envelopes: curves described through a family of other curves. The narrator praises its tangible examples and friendly presentation.
One selected video by Paralogical starts with the bright curve at the bottom of a mug and explains envelopes: curves described through a family of other curves. The narrator praises its tangible examples and friendly presentation.
Matt Ferraro’s written piece explains how a shaped acrylic sheet redirects light to form a deliberate image. Its account includes the mathematics, algorithms and false starts involved in making the object.
Freya Holmér’s “The Beauty of Bézier Curves” stood out not merely for polished graphics but for explaining why the curves matter in her work and connecting clean visuals to useful intuition.
Another selection asks for the most complicated phone unlock pattern. The creator makes the question precise and turns the search into a story involving number theory, induction and generalization.
The fifth selection presents a memorable proof related to Pick’s theorem and reflects on the different roles proofs can play. The narrator values the clarity of its central idea over production polish.
Honorable mentions
Selecting only five from so many submissions feels arbitrary, the narrator says. The larger purpose remains encouraging people to finish projects and share knowledge.
Selecting only five from so many submissions feels arbitrary, the narrator says. The larger purpose remains encouraging people to finish projects and share knowledge.
Among the honorable mentions is Noah Miller’s long explanation of Dirac’s belt trick, rotations and their connection to quantum mechanics. The narrator praises its patient treatment of a difficult subject.
Carl Turner’s video on the insolubility of the quintic also impressed him. He says it approached a proof he had been considering for his own video and motivated him to seek a different presentation.
Other recommended pieces cover the two-envelope problem, font rasterization, spinors, the number e and an ancient multiplication algorithm. The submissions include work in different languages and media.
The narrator also highlights explanations of Buffon’s needle, interactive work on complex numbers, and visual projects that stand out for their style. Technical detail and accessibility can complement each other.
Narrative and discovery
Narrative can make an online explanation memorable. Examples include stories connecting a lights-out puzzle to Gaussian elimination, a tile puzzle to Fibonacci numbers, and different settings to the Sierpiński triangle.
Narrative can make an online explanation memorable. Examples include stories connecting a lights-out puzzle to Gaussian elimination, a tile puzzle to Fibonacci numbers, and different settings to the Sierpiński triangle.
The video ends by encouraging viewers to explore the full playlist and accompanying blog post, where many excellent entries remain less widely known. The narrator thanks everyone who participated.
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